Civil Service Exam (Subprofessional) Numerical Ability — Decimals & Scientific NotationFlash Cards

What is the rule for adding and subtracting decimals?

When adding or subtracting decimals: 1) Align the decimal points vertically, 2) Add zeros to the right if needed to make equal decimal places, 3) Add or subtract as with whole numbers, 4) Place the decimal point in the answer directly below the aligned decimal points. Example: 12.5 + 0.35 = 12.50 + 0.35 = 12.85

How do you multiply decimals?

To multiply decimals: 1) Multiply as if they were whole numbers (ignore decimal points), 2) Count total decimal places in both factors, 3) Place decimal point in the product by moving left the same number of places. Example: 0.25 × 0.5 = 25 × 5 = 125, then place decimal 3 places from right = 0.125 (2 + 1 decimal places)

What is the process for dividing decimals?

To divide decimals: 1) Set up long division with dividend inside and divisor outside, 2) Move decimal point in divisor to the right to make it a whole number, 3) Move decimal point in dividend the same number of places, 4) Place decimal point in quotient directly above the new decimal point in dividend, 5) Divide as with whole numbers. Example: 0.4595 ÷ 0.05 becomes 45.95 ÷ 5 = 9.19

How do you convert a percentage to a decimal?

To convert a percentage to a decimal, move the decimal point two places to the left (or divide by 100). Examples: 25% = 0.25, 30% = 0.30, 1.25% = 0.0125. Remember that percent means 'per hundred', so you're dividing by 100.

What is the formula triangle for Percentage, Rate, and Base?

The PRB triangle shows: P (Percentage) at top, R (Rate) and B (Base) at bottom. Formulas: P = R × B, R = P/B, B = P/R. To use: cover what you're solving for, and the remaining shows the operation. P is associated with 'is', R with '%' or 'percent', B with 'of'.

What is 25% of 600?

Using P = R × B: P = 0.25 × 600 = 150. Always convert percentage to decimal first (25% = 0.25). This is a percentage problem where you're given the rate (25%) and base (600), solving for percentage.

400 is what percent of 2,000?

Using R = P/B: R = 400/2000 = 0.2 = 20%. This is a rate problem where you're given the percentage (400) and base (2000), solving for the rate. Convert the decimal result to percentage by multiplying by 100 or moving decimal point two places right.

210 is 30% of what number?

Using B = P/R: B = 210/0.30 = 700. This is a base problem where you're given the percentage (210) and rate (30%), solving for the base. Remember to convert percentage to decimal (30% = 0.30) before dividing.

What is 1/4 of 500?

Method 1: 1/4 × 500 = 500/4 = 125. Method 2: Convert to percentage: 1/4 = 25%, so 0.25 × 500 = 125. Both methods give the same result. Fractions can be converted to percentages or used directly in multiplication.

How do you solve percentage problems with fractions?

For fractions in percentage problems: 1) Convert mixed fractions to improper fractions, 2) Use the same PRB formulas (P = R × B, etc.), 3) When dividing fractions, multiply by the reciprocal, 4) Reduce final answers to lowest terms. Example: 1/2 is 3/4 of what number? → 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3

What is a ratio and how is it written?

A ratio is a comparison of two quantities of the same unit. It can be written in three ways: 1) Word form ('3 is to 1000'), 2) Fraction form (3/1000), 3) Colon form (3:1000). Example: ratio of 3 cm to 1000 cm can be written as 3:1000, 3/1000, or '3 is to 1000'.

What is the difference between ratio and rate?

Ratio compares two quantities of the SAME unit (3 cm to 1000 cm). Rate compares two quantities of DIFFERENT units (3 km/hr, 3 pesos/orange). Both use division, but rate always involves different units of measurement.

What is a proportion and how do you solve it?

A proportion is a statement that two ratios are equal (a:b = c:d). To solve: the product of extremes equals the product of means (a × d = b × c). Example: 3:x = 1:5 → 3 × 5 = x × 1 → x = 15. Cross multiply to find the missing term.

How do you read the decimal 176.304?

176.304 is read as 'one hundred seventy-six and three hundred four thousandths'. The whole number part (176) is read normally, 'and' represents the decimal point, and the decimal part (304) is read with its place value (thousandths, since it has 3 decimal places).

How do you round 67.678 to the nearest hundredth?

To round 67.678 to the nearest hundredth: Look at the thousandths place (8). Since 8 ≥ 5, round up by adding 1 to the hundredths place (7 becomes 8) and drop the digits after. Result: 67.68 (Note: some texts show 67.680 to emphasize the place value).

What happens when you multiply by powers of 10?

When multiplying by 10^n, move the decimal point n places to the RIGHT. Examples: 0.00095 × 1000 = 0.00095 × 10³ → move 3 places right = 0.95. When dividing by 10^n, move decimal point n places to the LEFT. Example: 69 ÷ 0.001 = 69 ÷ 10⁻³ = 69 × 10³ = 69,000.

What are direct and inverse proportions?

Direct proportion: As one variable increases, the other increases proportionally (ratio stays constant). Example: speed and distance with constant time. Inverse proportion: As one variable increases, the other decreases proportionally (product stays constant). Example: speed and time with constant distance.

How do you convert fractions to percentages?

Method 1: Get equivalent fraction with denominator 100. Example: 1/4 = 25/100 = 25%. Method 2: Divide and multiply by 100. Example: 3/8 = 0.375 × 100% = 37.5%. Use Method 1 for simple fractions, Method 2 for complex ones.

Solve: (0.16 × 0.4) + (0.17 × 0.5) + (0.18 × 0.6)

Calculate each product: 0.16 × 0.4 = 0.064, 0.17 × 0.5 = 0.085, 0.18 × 0.6 = 0.108. Add: 0.064 + 0.085 + 0.108 = 0.257. Remember to align decimal points when adding and count decimal places when multiplying.

If Mila has ₱15,000 and spends 25% on clothes, how much is left?

Amount spent: 15,000 × 0.25 = ₱3,750. Amount left: 15,000 - 3,750 = ₱11,250. Alternative: She has 75% left, so 15,000 × 0.75 = ₱11,250. Word problems require identifying what percentage represents and what operation to use.